Section 13.6a

The Unit Circle

The Unit Circle (like any circle) contains 360°

It’s called the Unit Circle because the length ofthe radius is 1

π/2

r = 1

Positive angle of rotation is counter clock-wise

Positive angle of rotation is counter clock-wise

π

The Unit Circle

x

y

1

x

y(1, 0)

1

ysin

((opposite)/(hypotenuse)((opposite)/(hypotenuse)

1

xcos

(adjacent) / (hypotenuse))(adjacent) / (hypotenuse))

Therefore, the coordinates of any point on the circle are: (cos , sin )Therefore, the coordinates of any point on the circle are: (cos , sin )

sin,cosP

Values of the Unit Circle

30o

r = 1sin 30o =

2

1,

2

3

cos 30o =

3

2

1

2

Values of the Unit Circle

45o

r = 1sin 45o =

cos 45o =

2

2,

2

2

2

2

2

2

Values of the Unit Circle

60o

r = 1sin 60o =

cos 60o =

2

3,

2

1

3

2

1

2

Values of the Unit Circle

r = 1

45o

sin 135o =

2

2

2

2cos 135o =

2

2,

2

2

-

Signs of Trigonometric Functions

Quadrant

I - All

AS

T C

All Students Take CalculusAll Students Take Calculus

++

+

Sin = Opp/HypCos = Adj/HypTan = Opp/Adj

-+

--

+++

II - Sin

III - TanIV - Cos

1.) using the unit circle convert each measure from degrees to radians

a) 150° b) 225° c) 480°

2.) using the unit circle convert each measure from radians to degrees

a) b) c)6

56

7 9

3.) use the unit circle to find the exact value of each

a) sin 120° b) tan 225°

4.) use the unit circle to find sine, cosine and tangent of each

a) b) 6

54

3

Homework

Worksheet 13-3B